Correct 'TransitionLayer' objects taking into account local distances

`geoCorrection(x, type, ...)`

- x
object of class

`Transition*`

- type
type of correction: "c", "r", or missing (only required for lonlat, see Details)

- ...
additional arguments passed to methods.

`multpl`

with correction factor (`TRUE`

) or corrected values (`FALSE`

, the default).`scl`

scale the correction values (default is`FALSE`

)

a 'Transition*' object

Geographic correction is necessary for all objects of the class Transition that are either: (1) based on a grid in a geographic (lonlat) projection and covering a large area; (2) made with directions > 4.

The function will correct for map distortion, as well as for diagonal connections between grid cells (which cover a longer distance than vertical or horizontal connections).

When working with lonlat grids, users should also anticipate whether they
will use methods based on either least-cost or random walks, and set the
type argument accordingly. In the case of least-cost distances, the
correction is only done in East-West direction. In the case of random walks
there should be an additional correction which reduces the conductance in
North-South direction (`type="r"`

).

The correction is done by dividing conductance values by the inter-cell
distance. Distances are calculated as great-circle distances for lonlat
grids (see function `[raster]{isLonLat}`

) and Euclidean distances for all other grids.

In the case of randomised shortest paths, the need for correction is somewhat in between these two correction methods. We have not developed an analytical solution for this problem yet. With very low values for theta, you may choose the correction for random walks, and for high values the one for least-cost paths. Users who want to work with intermediate values of theta are encouraged to experiment with different solutions.

The values are scaled to get values near 1 if the argument `scl`

is set to
TRUE. This is desirable for subsequent calculations involving random walk
calculations. Values are divided by the W-E inter-cell distance (at the
centre of the grid).

```
library("raster")
r <- raster(ncol=36,nrow=18)
r <- setValues(r,rep(1,times=ncell(r)))
tr <- transition(r, mean, directions=8)
#> The extent and CRS indicate this raster is a global lat/lon raster. This means that transitions going off of the East or West edges will 'wrap' to the opposite edge.
#> Global lat/lon rasters are not supported under new optimizations for 4 and 8 directions with custom transition functions. Falling back to old method.
# directly
tr1 <- geoCorrection(tr, type="c", multpl=FALSE)
tr1
#> class : TransitionLayer
#> dimensions : 18, 36, 648 (nrow, ncol, ncell)
#> resolution : 10, 10 (x, y)
#> extent : -180, 180, -90, 90 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs
#> values : conductance
#> matrix class: dsCMatrix
# the same, but with a separate correction matrix
trCorr <- geoCorrection(tr, type="c", multpl=TRUE)
tr2 <- tr * trCorr
tr2
#> class : TransitionLayer
#> dimensions : 18, 36, 648 (nrow, ncol, ncell)
#> resolution : 10, 10 (x, y)
#> extent : -180, 180, -90, 90 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs
#> values : conductance
#> matrix class: dsCMatrix
```